President Obama remains his party’s biggest moneymaker, bringing in tens of thousands of dollars per person at 79 Democratic fundraisers during his second term, but analysts say he has run into the embarrassing situation that also bedeviled his predecessor: vulnerable members of his own party keeping their distance.

Republicans have pounced on the fact that high-profile Democrats up for re-election, such as Sen. Mark Udall of Colorado, have opted not to appear with the president even when he is in their own backyard.

Other Democrats, such as Kentucky Senate hopeful Alison Lundergan Grimes, appear eager to enlist more popular figures to help raise money. Former President Bill Clinton appeared alongside Ms. Lundergan Grimes at an event in Lexington this month.

The White House and Democratic Party officials have responded by freezing reporters out of fundraisers to avoid unflattering stories, said Brendan Doherty, a political science professor at the U.S. Naval Academy and a scholar of presidents and fundraising.

“Even unpopular presidents are in great demand for fundraising, but more of their fundraisers tend to be closed to the press,” said Mr. Doherty, author of “The Rise of the President’s Permanent Campaign.” “And you get these occasional embarrassing stories where the candidate for whom they’re fundraising will appear at the fundraiser but won’t appear at the president’s appearance in the state.”

Mr. Udall appeared so determined not to give Colorado Republicans campaign fodder that he skipped a fundraiser in Denver last month with the president.

That event was open to the press, making it easier for reporters to latch onto the story that the Democratic senator opted to remain in Washington rather than be seen with Mr. Obama.

Even on vacation, the president has continued raking in money for his party. While at Martha’s Vineyard in Massachusetts, he headlined a Democratic Senatorial Campaign Committee event Monday and was joined by Sen. Edward J. Markey, Massachusetts Democrat, and other members of his party.

Mr. Obama blasted Republicans and claimed that Democratic leaders are not the reason for partisan gridlock in Washington.

“If you look at the leadership of Democrats in both the House and the Senate, they’re not ideological, they’re not proposing radical solutions,” Mr. Obama said. “They are common sense. They are pragmatic. That’s how we got health care passed. That’s why we’ve been able to make progress on an issue like climate change.”

Many other times, the president’s words to Democratic donors remain secret.

Mr. Obama has held at least 19 closed-door fundraisers this year, according to the Sunlight Foundation, which advocates greater transparency in government and among federal officials.